Apply Bevel/rounding to junction of two combined forms
I don't know whether you're using subdivision - so these approaches may not be your way.... (all the operations are under a subdivision modifier, level 1 or 2)




starting with a cube, add some edge loops (CtrlR), to support its sharp edges, and to halve its sides. Then cut the diagonals you can see, using the knife tool (K).
bevel the central vertex (CtrlShiftB)
inset the new face  (I) to make room for a bevel
extrude (E) the inset face
maybe scale the top face (in my case, Z is up, so that's SShiftZ), bevel (CtrlB) the edge at the turn to the extrusion, adjusting the profile with the mouse wheel to increase divisions, (you could do that, and change the profile and offset of the bevel at the bottom of the toolbar region while the tool is active, if necessary.)


But as you can see, that results in sharp turn, not very like the profile you illustrate, and there's not much room to move edge loops around.

So the bottom row in my illustration doesn't use beveling at all, and just tweaks the heights  and scales of the horizontal edge loops on the dome.

Edit mode>edge ..Alt select an edge loop

SShiftZ to scale it in XY

GG to slide the loop up and down without significantly altering the profile

GZ to move it up and down and alter the profile

If the subdivision modifier's' "Display modifier in Edit mode" box is checked, you can visually adjust the modifier's result to your profile. But be aware, if the subdivision level is changed, the profile may fatten or shrink.